Textbook Question
From a random sample of airplanes, the number of defects found in their fuselages are listed. Find the sample mean and the sample standard deviation of the data.
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.R.43
A student’s test grade of 75 represents the 65th percentile of the grades. What percent of students scored higher than 75?
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Understand the concept of percentiles: The 65th percentile means that 65% of the students scored less than or equal to the given grade (75 in this case).
Recognize that the remaining percentage of students scored higher than the 65th percentile. To find this, subtract the percentile value (65%) from 100%.
Set up the calculation as: \( 100\% - 65\% \).
Simplify the subtraction to determine the percentage of students who scored higher than 75.
Interpret the result: The final value represents the proportion of students who scored above the grade of 75.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentile
A percentile is a statistical measure that indicates the value below which a given percentage of observations fall. For example, if a student's score is at the 65th percentile, it means that 65% of the students scored below that score. Understanding percentiles helps in interpreting how a particular score compares to the rest of the data set.
Cumulative Distribution
A cumulative distribution function (CDF) shows the probability that a random variable takes on a value less than or equal to a specific value. In the context of percentiles, the CDF helps to determine the proportion of scores that fall below a certain threshold, which is essential for understanding how many students scored higher than a given score.
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Complementary Percentage
The complementary percentage refers to the portion of a population that exceeds a certain value. In this case, if 65% of students scored below 75, then 100% - 65% = 35% of students scored higher than 75. This concept is crucial for answering questions about relative performance in a statistical context.
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Related Practice
Textbook Question
The towing capacities (in pounds) of all the pickup trucks at a dealership have a bell-shaped distribution, with a mean of 11,830 pounds and a standard deviation of 2370 pounds. In Exercises 45– 48, use the corresponding z-score to determine whether the towing capacity is unusual. Explain your reasoning.
5,500 pounds
Textbook Question
In Exercises 7 and 8, use the data set shown in the table at the left, which represents the pollution indices (a unitless measure of pollution ranging from 0 to 100) for 24 U.S. cities. (Adapted from Numbeo)
Use a dot plot to display the data set. Describe any patterns.
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Textbook Question
In Exercises 21 and 22, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.
Textbook Question
In Exercises 27 and 28, find the range, mean, variance, and standard deviation of the sample data set.
Salaries (in dollars) of a random sample of teachers
62,222 56,719 50,259 45,120 47,692 45,985 53,489 71,534
Textbook Question
Describe the shape of the distribution for the histogram you made in Exercise 3 as symmetric, uniform, skewed left, skewed right, or none of these.
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